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Find the value of $x$ such that,
$3 \tan^2 60^\circ - x \sin^2 45^\circ + \frac{3}{4} \sec^2 30^\circ = 2 \cosec^2 30^\circ$
$3 \tan^2 60^\circ - x \sin^2 45^\circ + \frac{3}{4} \sec^2 30^\circ = 2 \cosec^2 30^\circ$
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$3 \tan^2 60^\circ - x \sin^2 45^\circ + \frac{3}{4} \sec^2 30^\circ = 2 \cosec^2 30^\circ$
$\Rightarrow 3(\sqrt{3})^2 - x(\frac{1}{\sqrt{2}})^2 + \frac{3}{4}(\frac{2}{\sqrt{3}})^2 = 2(2)^2$
$\Rightarrow 9 - \frac{x}{2} + 1 = 8$
$\Rightarrow x = 4$
$\Rightarrow 3(\sqrt{3})^2 - x(\frac{1}{\sqrt{2}})^2 + \frac{3}{4}(\frac{2}{\sqrt{3}})^2 = 2(2)^2$
$\Rightarrow 9 - \frac{x}{2} + 1 = 8$
$\Rightarrow x = 4$